Bulletin of Computational Applied Mathematics (Bull CompAMa)
Derivative-free method for bound constrained nonlinear monotone equations and its application in solving steady state reaction-diffusion problems
Octavio Batta, William La Cruz, Gilberto Noguera
We present a derivative-free algorithm for solving bound constrained systems of nonlinear monotone equations. The algorithm generates feasible iterates using in a systematic way the residual as search direction and a suitable step-length closely related to the Barzilai-Borwein choice. A convergence analysis is described. We also present one application in solving problems related with the study of reaction-diffusion processes that can be described by nonlinear partial differential equations of elliptic type. Numerical experiences are included to highlight the efficacy of proposed algorithm.
Keywords: nonlinear equations; derivative-free algorithm; monotone mapping; reaction-diffusion problems.
Cite this paper:
Batta O., La Cruz W., Noguera G., Derivative-free method for bound constrained nonlinear monotone equations and its application in solving steady state reaction-diffusion problems,
Bull. Comput. Appl. Math. (Bull CompAMa),
Vol. 4, No. 2, Jul-Dec, pp.71-93, 2016.